The article is wrong to call it "Common Core online testing". Common Core is short for Common Core State Standards [CCSS], and thus are a standard, not curriculum or tests. Tests and curricula can be Common Core-aligned, but the standards do not outline any specific test.

With that in mind, there are different CCSS tests out there from the usual corporations that produce school tests. States/school boards adopting CCSS are free to buy into any test that is CCSS aligned. Some are online, others are traditional.

Inevitably, schools will go with online tests because they will appear less expensive in terms of administering and grading. The efficacy of administering computerized tests and how that affects the outcome (particularly for writing and math) will be the new cultural bias for tests.

The two main consortia developing Common-Core-targeted testing are both aiming for computer-only. Among other things, it enables new question types that are still objectively scorable but have more flexibility than the traditional single-selection multiple choice question. (Although, all of the new question types that I know about are mouse/pointer-based, not requiring keyboards, so maybe they're talking about some other thing. Perhaps the subjective-scoring portions (i.e. the essays)?)

For the first 1-3 years, I believe, states/districts will have the option of paying extra for paper versions of the test. That's only a transitional option, though, and paper will be deprecated in favor of the online test. (One exception -- paper tests will be available indefinitely for students with special needs who can't take the test online.)

One of the big problems with online tests that we're seeing in some of our school districts is that many students don't have great typing or computer skills. Even though most students can probably type well enough to complete the tests, the extra mental challenge of typing is likely to artificially lower scores. So a test that purports to measure math skills might actually be measuring a combination of math skills + computer skills, and a school that's worked really hard to teach math might get docked because students haven't had a lot of computer experience.

This doesn't necessarily mean that online testing is a bad idea, but just one of the many things that we need to take into account.